Commutators spanning the matrices

Thread starter hkus10
Start date Mar 19, 2011
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Commutators Matrices

In summary, commutators spanning the matrices are a set of matrices that reveal important information about the relationships and properties of matrices. They are typically represented as [A, B] and are calculated by multiplying two matrices together and then subtracting the result from the product of the matrices in the opposite order. These commutators have real-world applications in physics, engineering, and computer science, such as in quantum mechanics, electrical engineering, and computer graphics.

Mar 19, 2011

hkus10

Let T be the set of all matrics of the form AB - BA, where A and B are nxn matrics. Show that span T is not Mnn.

1) does "span T is not Mnn" mean that Mnn does not span T?

Thanks

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Mar 19, 2011

Char. Limit

Gold Member

Looks to me like what it means is that T does not span Mnn, not the other way around.

1. What are commutators spanning the matrices?

Commutators spanning the matrices refer to a set of matrices that, when multiplied together, produce all possible combinations of matrices in a given set. They are used in linear algebra to show the relationships between matrices.

2. How are commutators spanning the matrices represented?

Commutators spanning the matrices are typically represented as square brackets [A, B], where A and B are the matrices being multiplied together. This notation is similar to the standard matrix multiplication notation.

3. What is the significance of commutators spanning the matrices?

The commutators spanning the matrices are significant because they reveal important information about the structure and properties of the matrices being studied. They can help identify patterns and relationships between matrices, which can be useful in solving problems in linear algebra.

4. How are commutators spanning the matrices calculated?

To calculate commutators spanning the matrices, first multiply the two matrices together according to the standard matrix multiplication rules. Then, subtract the result from the product of the matrices in the opposite order. The resulting matrix is the commutator spanning the matrices.

5. What are some real-world applications of commutators spanning the matrices?

Commutators spanning the matrices have various applications in physics, engineering, and computer science. They are used in quantum mechanics to study the behavior of subatomic particles, in electrical engineering to analyze circuits, and in computer graphics to create 3D transformations.